"I definitely feel like I'm proud of her, but at the same time I want her to keep going and do better and do more and do more," the 32-year-old Serena said of her big sister. "And then our relationship, we have just grown older, we are still really close. It's evolved, where it's evolved, I think in a good way."

Serena, the defending champion, could meet Venus in the third round if both get through their next matches.

The French Open is only Federer's third clay-court tournament this season. He reached the final in Monte Carlo but missed the Madrid tournament when his second set of twins, boys Leo and Lenny, was born.

His first match after their birth was a loss in Rome.

On Sunday, with the clay court hard and damp due to days of rain and overcast skies, the fourth-seeded Federer was back to himself, winning five of his 11 break points.

"I was happy seeing, getting early signs out of the match that I was actually playing well and I was going to get my chances I was looking for," Federer said. "My personal life, as we know, it's all great, so I'm happy the family is here."

Federer's twin girls, Myla Rose and Charlene Riva, will turn 5 in July. They were sitting in Federer's box along with his wife Mirka at the start.

The French Open is the only Grand Slam tournament to start on Sunday, and Federer played the second match on center court.

"I wasn't nervous, actually, going into the match. It's more just like those hints of fear, maybe yesterday, maybe this morning at one point, just for like five seconds, `Oh, I really hope I don't have to pack my bags today,' that kind of feeling," Federer said.

Serena Williams dictated most points in her match against Lim, a wild-card entry from France.

The top-seeded Serena is a 17-time major champion who was facing a woman making her Grand Slam debut. Still, there was a bit of shakiness from the 32-year-old American as she served out the final game, erasing four break points and needing five match points to close things.

"I was a little nervous, like I always am in my first round," Serena said. "It's kind of always hard for me to shake those nerves and go from there."

With the victory, Serena improved to 54-1 in first-round matches at majors. The only loss came at the 2012 French Open against 111th-ranked Virginie Razzano.

Also, Agnieszka Radwanska was able to reach the second round - once she got a handle on her serve.

Radwanska and Zhang Shuai traded breaks in the opening seven games of their match, but the third-seeded Pole finally held and won the final nine games to become the first player to reach the second round, winning 6-3, 6-0.

"So many breaks in a row," said Radwanska, who blamed her struggles on the wet court.